Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Presented at

Diagonal Representation of Density Matrix Using q-Coherent States

R. Parthasarathy, R. Sridhar

Published Jan 1, 2003• 1 citation
OpenAlex

Abstract

A q-analogue of the diagonal representation of the density matrix is derived using q-boson coherent states. The q-generalization of the self-reproducing property of ρ(z ,z ) and a self consistent self-reproducing kernel K(z ,z ) are obtained. Some applications to non-linear issues in optics are indicated

Related papers

$(q;l,λ)-$deformed Heisenberg algebra: representations, special functions and quantization

Mahouton Norbert Hounkonnou, Sama Arjika, Ezinvi Baloïtcha

This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements $ρ(z',z)$, derivedfrom $(q;l,λ)-$deformed boson coherent states.The induced $ρ(z',z)$ self-reproducing property with the associated self-reproducing kernel $K(z',z)$ is computed and analyzed. An explicit construction of novel classes of generalized continuous $(q;l,λ)-$Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.

arXiv:1301.7028•Jan 29, 2013•0 citations

Representation of Operators in Quantum Optics

Marvin M. Miller, Eli A. Mishkin

The invariance properties of the double-integral and diagonal representations of operators in terms of the coherent states are examined. It is shown that a unique diagonal representation always exists for bounded operators, hence for every density operator, and for unbounded operators which are polynomials in the boson creation and annihilation operators. The associated weight function $P(\ensuremath{\alpha})$ is a generalized function in the space ${Z}^{\ensuremath{'}}$. The physical significance of this result is discussed, with particular emphasis on the diagonal representation of the density operator of arbitrary radiation fields. A general formula for the weight function $P(\ensuremath{\alpha})$ is derived and is used to calculate the particular form of the weight function for several radiation fields of interest.

Physical Review•Dec 25, 1967•27 citations

Calculating Density Operator from Diagonal Coherent State Representation

Fan Hong-Yi, Huan Tu-Nan

By means of combining the coherent's properties with the normal product's properties we put forward to a formulation for obtaining density operators from Glauber-Suaaishan “P representation” and other non-diagonal representations directly in quantum optics.

Communications in Theoretical Physics•Jul 1, 1985•7 citations

Some new non-diagonal representations for density operators of optical fields

Hari Prakash, Naresh Chandra, Vachaspati

Some new non-diagonal representations for density operators of radiation in terms of coherent states are given. These involve only two integrations per mode. The weight functions are expressed in terms of coherence functions and of occupation number space matrix elements of the density operators. When a compact form of the weight function in the diagonal representation does not exist, one of these new representations may become preferable. One such example is discussed.

Journal of Physics A Mathematical Nuclear and General•Nov 21, 1974•0 citations

A diagonal representation of the quantum density matrix using q-boson oscillator coherent states

R. Parthasarathy, Radhakrishnan Sridhar

arXiv:math/0208128•Physics Letters A•Dec 1, 2002•16 citations

E.C.G.Sudarshan and his Diagonal Representation in Quantum Optics

Sobhan Kumar Sounda, Koushik Mandal

The essential of this monograph is to reproduce the results of Sudarshans paper Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams published in 1963. To go in that direction we also describe the linear harmonic oscillator and its algebraic equivalence with a single-mode quantized beam of light. Coherent states and their overcompleteness properties along with the diagonal representation of the density matrix are essential as a prerequisite to reproduce the result. Most of the textbooks meant for graduate students describe linear harmonic oscillators in great detail but they cryptically mention coherent states and their associated properties. So it is difficult for the students to understand the essence of Sudarshans paper which contains only seven equations. This monograph is written in such a lucid manner that without the help of experts one can understand it.

arXiv:2210.06224•Oct 12, 2022•0 citations
(q;l,λ)−(q;l,λ)-(q;l,λ)−deformed Heisenberg algebra: representations, special functions and quantization
This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements ρ(z′,z)ρ(z',z)ρ(z′,z), derivedfrom (q;l,λ)−(q;l,λ)-(q;l,λ)−deformed boson coherent states.The induced ρ(z′,z)ρ(z',z)ρ(z′,z) self-reproducing property with the associated self-reproducing kernel K(z′,z)K(z',z)K(z′,z) is computed and analyzed. An explicit construction of novel classes of generalized continuous (q;l,λ)−(q;l,λ)-(q;l,λ)−Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.
The invariance properties of the double-integral and diagonal representations of operators in terms of the coherent states are examined. It is shown that a unique diagonal representation always exists for bounded operators, hence for every density operator, and for unbounded operators which are polynomials in the boson creation and annihilation operators. The associated weight function $P(\ensuremath{\alpha})$ is a generalized function in the space ${Z}^{\ensuremath{'}}$. The physical significance of this result is discussed, with particular emphasis on the diagonal representation of the density operator of arbitrary radiation fields. A general formula for the weight function $P(\ensuremath{\alpha})$ is derived and is used to calculate the particular form of the weight function for several radiation fields of interest.
The essential of this monograph is to reproduce the results of Sudarshans paper Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams published in 1963. To go in that direction we also describe the linear harmonic oscillator and its algebraic equivalence with a single-mode quantized beam of light. Coherent states and their overcompleteness properties along with the diagonal representation of the density matrix are essential as a prerequisite to reproduce the result. Most of the textbooks meant for graduate students describe linear harmonic oscillators in great detail but they cryptically mention coherent states and their associated properties. So it is difficult for the students to understand the essence of Sudarshans paper which contains only seven equations. This monograph is written in such a lucid manner that without the help of experts one can understand it.